Midlands Graduate School Christmas Seminars
2012

The University of Nottingham, Jubilee Campus, Tuesday 18 December,
2012

Information and Programme

The Event

In addition to its yearly programme of taught courses on the mathematical
foundations of computing, the Midlands
Graduate School (MGS) holds an afternoon of Christmas Seminars. The
seminars are free and open to everyone.

The 2012 seminars will take place 14:00–17:30, 18 December,
A25 Business School South, at the University of Nottingham
Jubilee Campus. Directions for getting to Jubilee Campus can be found
here. Business School South is building 7 on the Jubilee Campus map available
off the same page. (A25 is actually located in the auditorium building,
number 8.)

Coffee will be served, so, for catering purposes, please let the
organiser, Henrik Nilsson, know if you intend to come by sending him
an e-mail
as soon as possible, preferably before 7 December.
Additionally, we plan to go for dinner afterwards. Likely Indian or
Chinese, depending on logistical factors. As it is close to Christmas,
restaurants tend to be busy with Christmas parties. Thus, it is
advisable to book ahead. So, if you would like to join for dinner
afterwards, again let the organiser know by e-mail, preferably
before 7 December, or it might not be possible to accommodate you.

Talk Details

Speaker: Sam Staton, University of Cambridge Computer Laboratory
(Joint work with Paul Levy)

Abstract: I will present joint work with Paul Levy on a foundation for
impure programming languages. I will explain how the equational theory of
LET-VAL in Standard ML can be seen as a non-commutative variant of Lambek's
multicategories. Using this structure I will demonstrate that type
constructions for impure languages — products, sums and functions
— can be characterized by universal properties, just as they can in the
pure setting. Our analysis gives a canonical status to earlier abstract ideas,
such as Moggi's monads, and puts them on a more syntactic level.

Abstract: Evolutionary algorithms mimic the natural evolution of
species to "evolve" good solutions for optimisation and design problems, using
operators like mutation, crossover, and selection. These popular search
heuristics have found wide-spread applications in many domains. Yet the reason
behind their success is often elusive, and it is not well understood when
these algorithms perform well and when not.

In the last 15 years the area of runtime analysis has emerged, using rigorous
mathematical methods for analysing the expected time until an evolutionary
algorithm finds a satisfactory solution for a given problem. I will give an
introduction into this area, showing how simple evolutionary algorithms can be
analysed. A particular focus will be on the role of the crossover operator,
and how it can improve performance.

Speaker: Roland Backhouse, University of Nottingham
(Joint work with Wei Chen and Joao Ferreira)

Abstract: Seven trees are one is a well-known type isomorphism due to
F.W.Lawvere. It led to the development by Marcelo Fiore (and others) of a
beautiful algebraic theory of type isomorphisms based on the notion of a rig.
However, although Fiore added a few more, the seven-trees isomorphism has
remained a relatively isolated example of intriguing type isomorphisms.

In an attempt to gain a better understanding, we posed ourselves the following
problem: Given a number n when is it possible to construct a type
T such that nTs are one? This problem was solved by Wei
Chen using the theory of cyclotomic polynomials and reported in his PhD thesis
(2012). As a result, we are now able to generate instances of such type
isomorphisms ad nauseum.

The seven-trees example was formulated by Dan Piponi as a simple
solitaire-like game with checkers played on a one-dimensional tape – a
Turing tape. This gave us the idea of using our understanding to formulate an
infinite collection of solitaire-like games. Since 2012 is the 100th
anniversary of Alan Turing's birth, we thought that a
competition
based on these “Turing-Tape Games” would be an appropriate way for
us to contribute to the celebration of Turing's legacy.

This talk is about our journey from seven-trees-in-one to the Turing-Tape
Games competition. We will also explain something of our goals and the
failures and successes of the competition.

Dinner

For dinner, we are we're heading to the South Indian restaurant
Kayal, the Nottingham branch: